College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.4 - Logarithmic Functions - 6.4 Assess Your Understanding: 41

Answer

domain: $(-\infty, 0) \cup (0, +\infty)$

Work Step by Step

RECALL: The logarithmic function $f(x) = \log_a{x}$ is defined only when $x \gt 0$. Thus, its domain is $x \gt 0$. This means that the function $f(x) = \log_2{(x^2)}$ is defined only when $x^2 \gt 0$. Note that the value of $x^2$ will always be greater than zero except when $x=0$. This means that the given function is undefined only when $x=0$. Thus, the domain of the given function is the set of all real numbers except 0. In interval notation, the domain is $(-\infty, 0) \cup (0, +\infty)$.
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